A new study explores the capability of third-generation gravitational-wave detectors, such as the Einstein Telescope and Cosmic Explorer, to detect scalar-induced gravitational waves (SIGWs). These waves, generated in the primordial universe, could offer a unique pathway to investigate primordial non-Gaussianity and parity violation. Researchers have developed a framework that considers contributions to the energy density spectrum of stochastic gravitational waves (SGWB) arising from scalar non-Gaussianity, quantified by the primordial bispectrum and trispectrum.

The particularity of this approach lies in the fact that the parity-odd component of the primordial scalar trispectrum induces circular polarization in the stochastic gravitational-wave background. This circular polarization would act as a direct signature of parity violation in the early universe. The analysis, based on simulated data from future interferometers, suggests that these instruments will be able to place competitive constraints on both the bispectrum and the scalar trispectrum (both its parity-even and parity-odd components).

Furthermore, the study has taken into account the contribution from astrophysical sources of gravitational waves, which could act as a "foreground" for the primordial signals. Despite the presence of this astrophysical foreground, the results indicate that future detectors will be able to effectively constrain cosmological parameters related to SIGWs, as well as astrophysical parameters. This highlights the potential of primordial gravitational waves as a cosmological tool to unravel fundamental properties of the early universe, such as the distribution of density fluctuations and parity symmetry.